Constancy of generalized Hodge-Tate weights of a local system

TL;DR

This paper proves that the multiset of generalized Hodge-Tate weights of a p-adic local system remains constant across a geometric family, demonstrating a form of rigidity in p-adic Hodge theory.

Contribution

It establishes the constancy of generalized Hodge-Tate weights in a geometric family of p-adic local systems, extending understanding of their rigidity.

Findings

Generalized Hodge-Tate weights are constant in a family of local systems.

Uses p-adic Riemann-Hilbert correspondence and Sen-Fontaine theory.

Provides basic properties of Hodge-Tate sheaves.

Abstract

Sen attached to each p-adic Galois representation of a p-adic field a multiset of numbers called generalized Hodge-Tate weights. In this paper, we discuss a rigidity of these numbers in a geometric family. More precisely, we consider a p-adic local system on a rigid analytic variety over a p-adic field and show that the multiset of generalized Hodge-Tate weights of the local system is constant. The proof uses the p-adic Riemann-Hilbert correspondence by Liu and Zhu, a Sen-Fontaine decompletion theory in the relative setting, and the theory of formal connections. We also discuss basic properties of Hodge-Tate sheaves on a rigid analytic variety.